# hwk1-sol - Due date Friday Math 116 Calculus Homework 1...

This preview shows pages 1–2. Sign up to view the full content.

Due date: June 19, 2009, Friday Math 116 Calculus – Homework # 1 – Solutions Remark: Solve all the problems. One of the problems, randomly chosen, will be graded. Q-1) Can the function f ( x,y ) = sin x sin 3 y 1 - cos( x 2 + y 2 ) be deﬁned at the origin in such a way that it becomes continuous there? If so, how? Solution: Limit of the expression as ( x,y ) goes to (0 , 0) along x -axis (or y -axis) is zero but limit along y = x direction is 1 / 2. So this function cannot be continuously extended to the origin. Q-2) Directional derivative of a function f ( x,y ) at the point ( - 1 , 1) in the direction ~ i + ~ j is 5, and in the direction ~ i - ~ j is - 5. Find the directional derivative of f ( x,y ) at ( - 1 , 1) in the direction of - ~ i - 2 ~ j . Solution: ~u = ( 1 2 , 1 2 ), ~v = ( 1 2 , - 1 2 ) and ~w = ( - 1 5 , - 2 5 ) are the unit vectors in the directions of ~ i + ~ j , ~ i - ~ j and - ~ i - 2 ~ j respectively. We are given that

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/29/2010 for the course MATH 116 taught by Professor Ahmetguloglu during the Spring '10 term at Bilkent University.

### Page1 / 3

hwk1-sol - Due date Friday Math 116 Calculus Homework 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online